Hurwitz equation
Given a length $k$ and a multiplier $m$, a Hurwitz equation^{} for a set of integers ${x}_{1},{x}_{2},\mathrm{\dots},{x}_{k}$ states that
$$\sum _{i=1}^{k}x_{i}{}^{2}=m\prod _{i=1}^{k}{x}_{i}.$$ |
There is no solution to the equation if $m>k$. Solutions can sometimes be found for $m\le k$ by starting from a $k$-long set of 1s. The Markov equation for the Markov numbers^{} has $k=m=3$.
References
- 1 R. K. Guy, Unsolved Problems in Number Theory^{} New York: Springer-Verlag 2004: D12
Title | Hurwitz equation |
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Canonical name | HurwitzEquation |
Date of creation | 2013-03-22 17:26:13 |
Last modified on | 2013-03-22 17:26:13 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 4 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 11J06 |
Classification | msc 11D72 |